Almost Everywhere First-Return Recovery

We show that for a wide class of σ-algebras 𝓐, indicatrices of 𝓐-measurable functions admit the same characterization as indicatrices of Lebesgue-measurable functions. In particular, this applies to functions measurable in the sense of Marczewski.

Concerning the measurable boundaries of a real function

C. Goffman, R. Zink (1960)

Fundamenta Mathematicae

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Measurable relations

C. Himmelberg (1975)

Fundamenta Mathematicae

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On the difference property of families of measurable functions

Rafał Filipów (2003)

Colloquium Mathematicae

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We show that, generally, families of measurable functions do not have the difference property under some assumption. We also show that there are natural classes of functions which do not have the difference property in ZFC. This extends the result of Erdős concerning the family of Lebesgue measurable functions.

On a theorem of C. Carathéodory

A. Alexiewicz, W. Orlicz (1955)

Annales Polonici Mathematici

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Gradients of Borel functions

B. Bongiorno, P. Vetro (1978)

Colloquium Mathematicae

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Almost uniform convergence for continuous parameters

Tibor Neubrunn (1978)

Mathematica Slovaca

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A remark on my paper “Regularly increasing functions in connection with the theory of $L^{* φ}$ -spaces”

W. Matuszewska (1965)

Studia Mathematica

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